The equation of the function is y = 4 sin( [tex]\frac{1}{2}[/tex] t - [tex]\frac{4}{3}\pi[/tex] ) - 2
Step-by-step explanation:
If the equation is y = A sin (B x + C) + D , where
- A is the amplitude
- The period is 2π/B
- C is the horizontal shift to the left (C is positive) or to right (C is negative)
- D is the vertical shift (D is positive) or down (D is negative)
∵ The amplitude is 4
∴ A = 4
∵ The period is 4π
∴ T= 4π ⇒ T = [tex]\frac{2\pi }{B}[/tex]
∵ The phase shift is [tex]-\frac{4}{3}\pi[/tex]
∴ C = [tex]-\frac{4}{3}\pi[/tex]
∵ The vertical shift is -2
∴ D = -2
Substitute these values in the y = A sin( [tex]\frac{2\pi }{T}[/tex] t + C) + D
∴ y = 4 sin( [tex]\frac{2\pi }{4\pi }[/tex] t - [tex]\frac{4}{3}\pi[/tex] ) - 2
- Simplify it
∴ y = 4 sin( [tex]\frac{1}{2}[/tex] t - [tex]\frac{4}{3}\pi[/tex] ) - 2
The equation of the function is y = 4 sin( [tex]\frac{1}{2}[/tex] t - [tex]\frac{4}{3}\pi[/tex] ) - 2
Learn more:
You can learn more about the trigonometric equations in brainly.com/question/2285189
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